The integer 'k', for which the inequality x² $$-$$ 2(3k $$-$$ 1)x + 8k² $$-$$ 7 > 0 is valid for every x in R, is :

Let p and q be two positive numbers such that p + q = 2 and p⁴+q⁴ = 272. Then p and q are roots of the equation :

If $$\alpha $$ and $$\beta $$ are the roots of the equation
2x(2x + 1) = 1, then $$\beta $$ is equal to :

If $$\alpha $$ and $$\beta $$ be two roots of the equation
x² – 64x + 256 = 0. Then the value of
$${\left( {{{{\alpha ^3}} \over {{\beta ^5}}}} \right)^{1/8}} + {\left( {{{{\beta ^3}} \over {{\alpha ^5}}}} \right)^{1/8}}$$ is :